| Summary: | We consider a two-dimensional Riemann problem for the unsteady transonic small
disturbance equation resulting in diverging rarefaction waves.
We write the problem in self-similar coordinates and we obtain a mixed
type (hyperbolic-elliptic) system.
Resolving the one-dimensional discontinuities in the far field, where
the system is hyperbolic, and using characteristics, we formulate the
problem in a semi-hyperbolic patch that is between the hyperbolic and
the elliptic regions. A semi-hyperbolic patch is known as a region where
one family out of two nonlinear families of characteristics starts on a
sonic curve and ends on a transonic shock. We obtain existence of a smooth
local solution in this semi-hyperbolic patch and we prove various properties
of global smooth solutions based on a characteristic decomposition using
directional derivatives.
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